
where \(T = \int _{0}^{\infty }t\, \gamma (t)\alpha (t)\)  is known as the transmissability of
the nodes [1]}. The above result was first
derived in [2]}, in absence of node deletion.
For uncorrelated networks, \(\mathrm {W}(k^{\prime }|k)=\mathrm {W}(k^{\prime })\)  and one has \(\hat{g}_k=\hat{g}~\forall ~k\ge 1\)  with
\(\hspace{-56.9055pt}\hat{g} &= \sum _{\sigma } \sigma \left[\mathrm {P}(\sigma ) - \sum _{k\ge 1} \mathrm {P}(\sigma |k)\frac{k\mathrm {P}(k)}{{{\langle }k {\rangle }}}\int _{0}^{\infty }t\, \gamma (t) \left(1 - \alpha (t)\hat{g}\right)^{k-1}\right]\nonumber \equiv f(\hat{g})\) 
